Polylogarithmic root bound for sparse trinomials over finite fields

Let $p\geq 3$ be prime, let $\gamma,e_2,e_3\in\{1,\ldots,p-2\}$ satisfy $e_3>e_2>0$ and $\gcd(e_2,e_3,p-1)=1$, and consider the trinomial

$$\gamma+x^{e_2}+x^{e_3}.$$

Polylogarithmic root-bound conjecture. There is an absolute constant $c\geq 1$ such that this trinomial has no more than $(\log p)^c$ roots in $\mathbb{F}_p$.

This conjecture proposes an upper bound for the number of roots of normalized trinomials over prime finite fields, in contrast with the experimentally motivated possibility of trinomials having on the order of $\sqrt p$ roots. Its status is not resolved by the supplied source context.